A locally adjustable quadric Catmull-Rom spline surface and its shape optimization(局部可调的四次Catmull-Rom样条曲面及其形状优化)

Abstract

The shape of the cubic Catmull-Rom spline cannot be adjusted locally when the control points remain unchanged. In order to meet the needs of the shape design of interpolation surfaces in practical engineering problems, a quadric Catmull-Rom spline surface with local parameters is presented, and two schemes for optimizing the shape of the quadric Catmull-Rom spline surface are given. The results show that the quadric Catmull-Rom spline surface not only inherits the interpolation and continuity property of the cubic Catmull-Rom spline surface, but also allow us to use the parameters contained to adjust its shape locally or globally. By determining the optimal values of the parameters, the desired smooth and shape-preserving quadric Catmull-Rom spline surface can be obtained. The proposed quadric Catmull-Rom spline surface and its shape optimization schemes provide methods for the construction of interpolation surfaces.(当控制顶点保持不变时，无法对三次Catmull-Rom样条曲面的形状进行局部调整。为满足实际工程对插值曲面形状设计的要求，给出了一种含局部参数的四次Catmull-Rom样条曲面，并讨论了2种对四次Catmull-Rom样条曲面形状进行优化的方案。结果表明，四次Catmull-Rom样条曲面不仅继承了三次Catmull-Rom样条曲面的插值性与连续性，而且容易利用所含的参数对曲面形状进行局部或整体调整，通过计算所含参数的最优值获得尽可能光顺和尽可能保形的四次Catmull-Rom样条曲面，为插值曲面的构造提供了方法。)

Keywords

• catmull-rom spline(catmull-rom样条)
• interpolation surface(插值曲面)
• local adjustment(局部调整)
• smoothness(光顺)
• shape-preserving interpolation(保形插值)